[R-sig-ME] Interpreting the output of summary() of a glmer-object

[Hans Ekbrand]

Dear list,

First, I have a very simple question. In the summary output of a
glmer-object, What does the "Variance" and "Std.Dev" mean for the
Random effects? What is the scale for these measures?

load(url("http://sociologi.cjb.net/temp/a.strange.df.RData"))
my.fit.1 <- glmer(MV744A ~ (1|MV024), data = a.strange.df, family = "binomial")
summary(my.fit.1)

Generalized linear mixed model fit by the Laplace approximation 
Formula: MV744A ~ (1 | MV024) 
   Data: a.strange.df 
   AIC   BIC logLik deviance
 76209 76227 -38102    76205
Random effects:
 Groups Name        Variance Std.Dev.
 MV024  (Intercept) 0.40558  0.63685 
Number of obs: 73601, groups: MV024, 29

Fixed effects:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept)  -1.4187     0.1191  -11.91   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

I think that I understand that if the Variance term, here 0.40558 is
low relative to the Std.Dev, there is not much variation caught by the
random term (in this case where the random term represents "Regions",
few Regions would then significantly differ from the grand mean). Here
we have a big underlying n, which might explain that most Regions did
signficantly differ from the mean.

dotplot(ranef(my.fit.1, postVar = TRUE))


Secondly, after adding several fixed terms, each with a substantial effect, I
would (given my vague understanding of what the "Variance" term means)
expect the "Variance" of the random effect to decrease, but on the
contrary it increased:

summary(my.fit.5 <- glmer(MV744A ~ (1|MV024) + MV025 + MV106 + MV012 + MV130, data = a.strange.df, family = "binomial"))

Generalized linear mixed model fit by the Laplace approximation 
Formula: MV744A ~ (1 | MV024) + MV025 + MV106 + MV012 + MV130 
   Data: a.strange.df
   AIC   BIC logLik deviance
 73327 73483 -36646    73293
Random effects:
 Groups Name        Variance Std.Dev.
 MV024  (Intercept) 0.46855  0.6845  
Number of obs: 73560, groups: MV024, 29

Fixed effects:
                             Estimate Std. Error z value Pr(>|z|)    
(Intercept)                -0.7491070  0.1343065   -5.58 2.44e-08 ***
MV025Rural                  0.4423018  0.0198776   22.25  < 2e-16 ***
MV106Primary               -0.1829852  0.0306670   -5.97 2.42e-09 ***
MV106Secondary             -0.5743379  0.0263945  -21.76  < 2e-16 ***
MV106Higher                -1.2945147  0.0385589  -33.57  < 2e-16 ***
MV012                      -0.0145262  0.0008938  -16.25  < 2e-16 ***
MV130Muslim                 0.3079549  0.0276753   11.13  < 2e-16 ***
MV130Christian             -0.2949242  0.0431780   -6.83 8.47e-12 ***
MV130Sikh                  -0.2605808  0.1087276   -2.40  0.01655 *  
MV130Buddhist/Neo-Buddhist -0.0139619  0.0830028   -0.17  0.86642    
MV130Jain                  -0.3624429  0.1909181   -1.90  0.05764 .  
MV130Jewish                -8.9103460 63.6027289   -0.14  0.88859    
MV130Parsi/Zoroastrian     -9.6231061 90.8921529   -0.11  0.91568    
MV130No religion           -0.5553414  0.7918028   -0.70  0.48308    
MV130Donyi polo             0.7034558  0.2266543    3.10  0.00191 ** 
MV130Other                 -0.0718436  0.0890363   -0.81  0.41972    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Sure, the Std.Dev of the random effect also increased (from 0.63685 to
0.6845) but still, isn't the increase of the variance of random effect
(from 0.40558 to 0.46855) rather odd here?

How do you interpret an increase in the random effect after adding
perfectly fine explanatory fixed terms to the model?

BTW. The dependent variable MV744A measures an attitude, and MV025 is
type of area (Urban/Rural), MV106 is educational level, MV012 is age,
MV130 is religion. 

The caterpillar plot for my.fit.5, shows all regions except 3 of them
differ signifcantly from the mean, even when controlling for the fixed
terms.

dotplot(ranef(my.fit.5, postVar = TRUE))

Any hints, or reading tips, greatly appreciated.

Kind regards,

--
Hans Ekbrand
Department of sociology and workscience
University of Gothenburg, Sweden.